What do “sell to open cover” and “sell to open uncovered” mean?

“Sell to open cover” means you own the underlying stock and are starting a new option position by selling a covered call. That means that the buyer of the call can demand your stock at any time at the strike price. 

“Sell to open uncovered” means you do not own the stock and you are starting a new option position by selling a call.  Selling a call without owning the stock is a risky proposition. The most you can make is the premium you collect for selling the call, and the risk is very high. If the stock spikes, you will have to buy it in the open market and then sell it at the strike price. If the stock takes off, you’ll likely be buying the stock at a much higher price than the strike price you’ll be selling it at.